Sphere on a Flat Plane: 3 Points of Contact?

[CheesyPeeps]

I've been reading about how much of a sphere actually touches a flat plane (spheres are very interesting things, it turns out!). Mathematically, a perfect sphere has only one point of contact, meaning that the area of this contact is infinitely small(?), but as physicists, we know that there must be three points of contact for the sphere to be at rest. Therefore, we can say that three atoms need to touch the flat plane for the sphere to be at rest.

My question is whether this three-atom rule is the same for any size of sphere, or does it change as sphere circumference increases/decreases?

 

[Mycroft_1058]

Good question, Mycroft...Hmmmm

(Long story short me and Cheesy Peeps are best friends and this is kinda an in-joke)

 

[nuclearhead]

If you zoom into a billiard ball it won't look very smooth at all. It will look very lumpy. Also you will find that it is not as solid as it appears. So when it is resting on a surface (which will be equally lumpy) zoomed up close it would look more like a sponge resting on another sponge. There will not actually be any points of contact since the repulsive force between electrons in the atoms will keep everything separated. But there will be many close atoms.

On the other hand, if you are talking mathematically, then you can imagine an enormous perfect spherical polyhedron made of triangles. And then mathemat ically it could be at rest if a triangular face lay on the surface of a flat plan. It could also theoretically balance on one or two points but that would be an unstable position.

 

[anorlunda]

Curious, we had the identical question yesterday.

It depends on the materials of the sphere and the flat surface of course. They will both deform.